Least Common Multiple (LCM) of 107 and 197
The least common multiple (LCM) of 107 and 197 is 21079.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 107 and 197?
First, calculate the GCD of 107 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 197 = 0 remainder 107 |
| 2 | 197 ÷ 107 = 1 remainder 90 |
| 3 | 107 ÷ 90 = 1 remainder 17 |
| 4 | 90 ÷ 17 = 5 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 82 | 12546 |
| 37 and 114 | 4218 |
| 137 and 150 | 20550 |
| 51 and 102 | 102 |
| 123 and 72 | 2952 |